In multiple access communications, multiple user devices transmit signals over a single communications channel to a receiver. These signals are superimposed, forming a combined signal that propagates over that channel. The receiver then performs a separation operation on the combined signal to recover one or more individual signals from the combined signal. For example, each user device may be a cell phone belonging to a different user and the receiver may be a cell tower. By separating signals transmitted by different user devices, the different user devices may share the same communications channel without interference.
A transmitter may transmit different symbols by varying a state of a carrier or subcarrier, such as by varying an amplitude, phase and/or frequency of the carrier. Each symbol may represent one or more bits. These symbols can each be mapped to a discrete value in the complex plane, thus producing Quadrature Amplitude Modulation, or by assigning each symbol to a discrete frequency, producing Frequency Shift Keying. The symbols are then sampled at the Nyquist rate, which is at least twice the symbol transmission rate. The resulting signal is converted to analog through a digital to analog converter, and then translated up to the carrier frequency for transmission. When different user devices send symbols at the same time over the communications channel, the sine waves represented by those symbols are superimposed to form a combined signal that is received at the receiver.
A conventional approach to produce a multiple access signal involves using Direct Sequence Spread Spectrum (DSSS). In DSSS, each user is provided with a code sequence, which has the customary representation by 0 or 1. This code sequence is subsequently translated to a bipolar sequence, represented by values of 1 and −1. The complex symbols mentioned earlier are then multiplied by this bipolar sequence, and subsequently sampled at the Nyquist rate, converted to analog and translated to the carrier frequency for transmission. The receiver will translate the signal to complex baseband and sample at the Nyquist rate. The receiver is also provided with the code sequence, and multiplies by the bipolar sequence. In this case, a PN code is generated from a deterministically-produced pseudo-random sequence that may be reproduced by the receiver. A bit of the PN code is known as a chip, and is provided at a chip rate that is usually a multiple of the symbol rate of the baseband signal so as to spread the original signal in frequency out to the bandwidth of the chip rate. For the above-described simple case, a user device modulates each signal with the PN code either by applying a phase shift to the signal (i.e., multiplying the signal by −1) or not (i.e., multiplying the signal by +1) at each chip. The combined signal received by the receiver is a superposition of the spread signals sent by each user device at the same time.
In DSSS, the receiver may despread the combined signal it receives and recover signals sent by a particular user device by computing a cross-correlation between a sequence of symbols from the spread signal with the PN code of the particular user device. The result of the cross-correlation is either (i) a large positive or negative number that indicates an original symbol sent by the particular user device at some time or (ii) a small positive or negative number indicating no symbol sent from that user device at that time.